What is obtained by subtracting the sum of the first (160) natural numbers from the sum of the first (200) natural numbers?
Answer and explanation
Correct answer: 7220
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{200}=\frac{200\times201}{2}=20100\) and \(S_{160}=\frac{160\times161}{2}=12880\). Therefore, the required difference is \(20100-12880=7220\). It is also the sum of the numbers from 161 to 200, so an option such as 7120 is incorrect. Exam tip: You can verify such a difference by recognising the remaining sequence from 161 to 200.
Frequently asked questions
What is the correct answer to this question?
7220
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{200}=\frac{200\times201}{2}=20100\) and \(S_{160}=\frac{160\times161}{2}=12880\). Therefore, the required difference is \(20100-12880=7220\). It is also the sum of the numbers from 161 to 200, so an option such as 7120 is incorrect. Exam tip: You can verify such a difference by recognising the remaining sequence from 161 to 200.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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